Multi-antennas techniques have become very popular to increase the throughput and/or the performance of wireless communications systems, especially in third-generation mobile communications networks, in new generations of wireless local area networks like Wi-Fi (Wireless Fidelity), and in broadband wireless access systems like WiMAX (Worldwide Interoperability for Microwave Access).
In MIMO systems, transmitter Tx, as well as receiver Rx are equipped with multiple antennas. As illustrated in FIG. 1, the transmitter Tx and the receiver Rx are both equipped, for example, with respectively a first and a second transmit antennas, Tx1 and Tx2, and a first and a second receive antennas, Rx1 and Rx2.
Among the numerous schemes proposed in the literature for transmissions using multiple antennas, spatial multiplexing model is one of the most popular ones which have been included in the specification of the WiMAX standard based on OFDMA (Orthogonal Frequency-Division Multiple Access).
In spatial multiplexing for transmission over two transmit antennas, Tx1 and Tx2, a signal s is fed into the transmitter Tx, which performs, for example, coding and modulation to provide two independent complex modulation symbols: a first symbol s1 and a second symbol s2. Each symbol belongs to a given signal constellation according to the modulation technique used, as well known by skilled in the art person. These two symbols, s1 and s2, are then simultaneously and respectively transmitted on the first and second transmit antennas, Tx1 and Tx2, during a time slot t corresponding to a given symbol period, through a channel defined by its channel matrix H. The transmit signal s can be expressed mathematically in a vector form, as it is exactly done for example in the WiMAX standard specification, as:
  s  =            [                                                  s              1                                                                          s              2                                          ]        .  
At the receiver side, the symbols are captured by the two receive antennas, Rx1 and Rx2, and demodulation and decoding operations are performed. The received signal y, received during time slot t, can be theoretically expressed in matrix form as:
                                          y            =                                          [                                                                                                    y                        1                                                                                                                                                y                        2                                                                                            ]                            =                                                                                          [                                                                                                                                  h                              11                                                                                                                                          h                              12                                                                                                                                                                                          h                              21                                                                                                                                          h                              22                                                                                                                          ]                                        ⁡                                          [                                                                                                                                  s                              1                                                                                                                                                                                          s                              2                                                                                                                          ]                                                        +                                      [                                                                                                                        n                            1                                                                                                                                                                            n                            2                                                                                                                ]                                                  =                                  Hs                  +                  n                                                              ,                ⁢                                                      (        1        )            where:                y1 and y2 respectively represent the signals received on the first and the second receive antennas;        n1 and n2 respectively represent the noise terms affecting the signals on the first and second receive antenna; and        the coefficients hij represent the propagation channel response (attenuation and phase) between the jth transmit antenna Txj and the ith receive antenna Rxi, j and i being integers.        
To recover the transmitted signal s from the received signal y, the receiver Rx seeks, among all the possible transmitted symbols belonging to the signal constellation used at the transmitter side for the first symbol s1 and the second symbol s2, the most probable transmitted signal ŝ given the received signal y.
Such a model is very general and encompasses in particular:                Single-carrier transmission using spatial multiplexing such as for instance the BLAST (Bell-Labs Layered Space-Time) system described in the article entitled “layered space-time architecture for wireless communication in a fading environment when using multi-elements antennas”, in Bell Labs Technology Journal, Autumn 1996, which is incorporated by reference.        OFDM (Orthogonal Frequency Division Multiplexing) and OFDMA transmissions using spatial multiplexing in which case the model applies on a subcarrier per subcarrier basis;        CDMA (Code Division Multiple Access) transmissions using spatial multiplexing in which case the model applies for instance after classical rake receiver.        
Further, the description focuses on devices capable of receiving such spatially multiplexed signals.
Designing practical receivers for signals transmitted using the spatial multiplexing remains a real challenge. Indeed, designing an optimal receiver, that is to say a receiver minimizing the probability of decoding error on an estimated transmitted signal, is not trivial to be done in practice though its solution can be very simply stated: the most probable transmitted signal ŝ given the received signal y is the one minimizing the following Euclidean norm m(s)=∥y−Hs∥2 (2).
Let us note
            s      ^        =          [                                                                  s                ^                            1                                                                                          s                ^                            2                                          ]        ,where m(ŝ)=∥y−Hŝ∥2 is the minimum of the Euclidean norm m(s) and, ŝ1 and ŝ2 are respectively the most probable transmitted first and second symbols.
This minimization can theoretically be achieved by using the Maximum Likelihood (ML) method, which includes performing an exhaustive search over all the possible transmitted symbols belonging to the signal constellation, to find the most probable transmitted signal ŝ minimizing the Euclidean norm.
But this requires a receiver capable of testing M2 symbols hypotheses, where M is the size of the signal constellation used at the transmitter Tx side for the first and second symbols s1 and s2, and unfortunately, this becomes rapidly impossible or impractical due to the huge number of hypotheses to be tested. For instance, 4096 and 65536 hypotheses have to be tested for respectively a 64-QAM (Quadrature Amplitude Modulation) and 256-QAM constellations.
Several receivers have been proposed in the literature to try to solve this intricate problem at a reasonable complexity, yet all suffer from rather limited performance.
Among the most important ones, several receivers are based on interference cancellation approaches, or on iterative detection.
For example, the application US2005/0265465 concerning “MIMO decoding” and which is incorporated by reference, proposes a receiver which decodes iteratively the symbols sent via each transmit antenna. In each stage of processing, the receiver estimates a first symbol, removes the estimated first symbol of the received signal to give a first interference-cancelled received signal, soft-estimates a second symbol from the first interference-cancelled received signal, and provides a symbol estimate error term, for example by computing the probability of error in decoding the symbols. The decoding may be iterated a number of times.
But the performance of such a receiver is far from optimal since it is prone to error propagation phenomenon, and tends to increase the latency of the decoder since the decoder shall perform several decoding passes before providing an estimate of the transmitted signal.